{
  "id": "1709.06273",
  "version": "v1",
  "published": "2017-09-19T07:16:39.000Z",
  "updated": "2017-09-19T07:16:39.000Z",
  "title": "Effective Grothendick-Witt motives of smooth varieties",
  "authors": [
    "Andrei Druzhinin"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1601.05383",
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "The category of effective Grothendick-Witt-motives (and Witt-motives) of smooth varieties in a similar way as Voevodsky category of motives $DM^-_{eff}(k)$, starting with some category of GW-correspondences (and Witt-correspondences) over a perfect field $k$, $char\\,k\\neq 2$, is defined. The functor $M^{GW}_{eff}\\colon Sm_k\\to DM^{GW}_{eff}(k)$ of Grothendick-Witt-motives of smooth varieties is computed and it is proved that for any smooth variety $X$ and homotopy invariant sheave with GW-transfers $\\cal F$ $$ Hom_{DM^{GW}_{eff}(k)}(M^{GW}_{eff}(X), \\mathcal F[i]) \\simeq H^i_{Nis}(X,\\mathcal F) $$ naturally in $X$ and $\\cal F$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-19T07:16:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smooth variety",
      "effective grothendick-witt motives",
      "homotopy invariant sheave",
      "similar way",
      "grothendick-witt-motives"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}